Berezin integral

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In mathematical physics, a Berezin integral is a way to define "integration" for functions of Grassmann variables. It is not an integral in the usual sense; it is called "integration" for convenience, since it is used in physics in a parallel manner to ordinary integration. It is named after the Russian mathematician Felix Berezin.

The Berezin integral is defined to be a linear functional with the following properties:

  • \int d\theta\, 1 = 0
  • \int d\theta\, \theta = 1

These two properties uniquely determine the map, because every function of a Grassmann variable is either constant or linear.

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